We study the long-term evolution of two or more stellar black holes (BHs) on initially separated but unstable circular orbits around a supermassive BH (SMBH). Such a close-packed orbital configuration can naturally arise from BH migrations in the AGN disk. Dynamical instability of the orbits leads to recurring close encounters between two BHs, during which the BH separation r _p becomes less than the Hill radius R _H. In rare very close encounters, a tight merging BH binary can form with the help of gravitational wave emission. We use N-body simulations to study the time evolution of close encounters of various degrees of closeness. For a typical “SMBH+2BH” system, the averaged cumulative number of close encounters (with r _p ≲ R _H) scales approximately as ∝ t ^0.5. The minimum encounter separation r _p follows a cumulative distribution P(<r _p) ∝ r _p for r _p ≪ R _H. We obtain a semi-analytical expression for the averaged rate of binary captures that lead to BH mergers. Our results suggest that close-packed BHs in AGN disks may take a long time (≳10⁷ orbits around the SMBH) to experience a sufficiently close encounter and form a bound binary. This time can be shorter if the initial BH orbits are highly aligned. The BH binary mergers produced in this scenario have high eccentricities when entering the LIGO band and broad distribution of orbital inclinations relative to the original AGN disk. We explore the effects of the gas disk and find that simple gas drags on the BHs do not necessarily lead to an enhanced BH binary capture rate.

中文翻译：

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AGN 盘中紧密堆积的恒星黑洞的长期演化：通过近距离接触形成并合黑洞双星

我们研究了两个或多个恒星黑洞 (BH) 在最初分离但围绕超大质量黑洞 (SMBH) 的不稳定圆形轨道上的长期演化。这种紧密堆积的轨道配置自然会产生于 AGN 盘中的 BH 迁移。轨道的动力学不稳定性导致两个 BH 之间反复发生近距离接触，在此期间 BH 分离r _p变得小于 Hill 半径 R _哈。在罕见的非常接近的相遇中，紧密合并的 BH 双星可以在引力波发射的帮助下形成。我们用否- 身体模拟来研究不同程度的近距离接触的时间演变亲密. 对于典型的“SMBH+2BH”系统，近距离接触的平均累积次数（与r _≲ _ R _H ) 大约为 ∝吨 ^0.5。最小相遇间隔r _p服从累积分布P(<r _p ) ∝r _为_r _≪ _ R _哈。我们获得了导致 BH 合并的二进制捕获平均速率的半解析表达式。我们的结果表明，AGN 盘中的密排 BH 可能需要很长时间（围绕 SMBH ≳10 ⁷轨道）才能经历足够近的相遇并形成束缚双星。如果初始 BH 轨道高度对齐，这个时间可以更短。在这种情况下产生的 BH 双星合并在进入 LIGO 波段时具有高偏心率，并且相对于原始 AGN 盘具有广泛的轨道倾角分布。我们探索了气盘的影响，发现 BH 上的简单气体阻力不一定会导致 BH 双星捕获率提高。